The Fourth-order dispersive nonlinear Schrödinger equation: orbital stability of a standing wave

2015/05/29 by Fábio Natali, Natali, Fábio, Ademir Pastor +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1506.00023

Abstract

Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schrödinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context of Hamiltonian systems. The main result is established by constructing a suitable Lyapunov function.

Cited by

• Existence and stability for traveling waves of fourth order semilinear wave and Schrodinger equations
• Dynamics of solutions in the 1d bi-harmonic nonlinear Schrödinger equation
• Some remarks on a minimization problem associated to a fourth order nonlinear Schrödinger equation
• On the orbital stability of periodic snoidal waves for the ϕ⁴-equation

Related

• On the orbital stability of solitary waves for the fourth order nonlinear Schrödinger equation
• Orbitally stable standing waves of a mixed dispersion nonlinear Schrödinger equation
• Existence and orbital stability of standing waves for the 1D\n Schr "odinger-Kirchhoff equation
• Orbital stability of standing waves of some m-coupled nonlinear Schrodinger equations
• Instability of standing waves for a system of nonlinear Schrödinger equations in a degenerate case